Millisecond Oscillations in X-Ray Binaries

Submitted to the Annual Review of Astronomy and Astrophysics; to appear September 2000 MILLISECOND OSCILLATIONS IN X-RAY BINARIES M. VAN DER KLIS Astronomical Institute “Anton Pannekoek”, University of Amsterdam Kruislaan 403, 1098 SJ Amsterdam, The Netherlands E-mail: [email protected] The first millisecond X-ray variability phenomena from accreting compact objects have recently been discovered with the Rossi X-ray Timing Explorer. Three new phenomena are observed from low-mass X-ray binaries containing low-magnetic- field neutron stars: millisecond pulsations, burst oscillations and kiloHertz quasi- periodic oscillations. Models for these new phenomena involve the neutron star spin, and orbital motion closely around the neutron star and rely explicitly on our understanding of strong gravity and dense matter. I review the observations of these new neutron-star phenomena and possibly related ones in black-hole candidates, and describe the attempts to use them to perform measurements of fundamental physical interest in these systems. 1 Introduction The principal motivation for studying accreting neutron stars and black holes is that these objects provide a unique window on the physics of strong gravity and dense matter. One of the most basic expressions of the compact- ness of these compact objects is the short (0.1–1msec) dynamical time scale characterizing the motion of matter under the influence of gravity near them. Millisecond variability will naturally occur in the process of accretion of matter onto a stellar-mass compact object, an insight that dates back to at least Shvartsman (1971). For example, hot clumps orbiting in an accretion disk around black holes and neutron stars will cause quasi-periodic variability on time scales of about a millisecond (Sunyaev 1973). Accreting low-magnetic field neutron stars will reach millisecond spin periods, which can be detected when arXiv:astro-ph/0001167v1 11 Jan 2000 asymmetric emission patterns form on the star’s surface during X-ray bursts (Radhakrishnan & Srinivasan 1984, Alpar et al. 1982; Shara 1982, Livio & Bath 1982, see also Joss 1978). These early expectations have finally been verified in a series of discoveries with NASA’s Rossi X-Ray Timing Explorer (RXTE; Bradt et al. 1993) within 2.5 years after launch on 30 December 1995. In this review, I discuss these newly discovered phenomena and the attempts to use them to perform measurements of fundamental physical interest. I concentrate on millisecond oscillations, periodic and quasi-periodic variations in X-ray flux with frequencies exceeding 102.5 Hz, but I also discuss their re- lations to slower variability and X-ray spectral properties. Millisecond oscillations have so far been seen nearly exclusively from low-magnetic-field neutron 1 stars, so these will be the focus of this review, although I shall compare their phenomenology to that of the black-hole-candidates ( 6-7). § Accreting neutron stars and black holes occur in X-ray binaries (e.g., Lewin et al. 1995a). In these systems matter is transferred from a normal (’donor’) star to a compact object. Thermal X-rays powered by the gravitational po- tential energy released are emitted by the inner regions of the accretion flow and, if present, the neutron star surface. For a compact object with a size of order 101 km, 90% of the energy is released in the inner 102 km. It is with this inner emitting region that we shall be mostly concerned∼ here. Because accreting low-magnetic-field neutron stars are mostly found in low-mass X-ray binaries (in which the donor star has a mass of <1M⊙) these systems will be the ones we focus on. The mass transfer usually occurs by way of an accretion disk around the compact object. In the disk the matter moves in near-Keplerian orbits, i.e., with an azimuthal velocity that is approximately Keplerian and a radial velocity much smaller than this. The disk has a radius of 105−7 km, depending on the binary separation. The geometry of the flow in the inner emitting regions is uncertain. In most models for accretion onto low-magnetic-field neutron stars (e.g., Miller et al. 1998a) at least part of the flow extends down into the emitting region in the form of a Keplerian disk. It is terminated either at the radius R of the star itself, or at a radius rin somewhat larger than R, by for example the interaction with a weak neutron-star magnetic field, radiation drag, or relativistic effects. Within rin the flow is no longer Keplerian and may or may not be disk-like. Both inside and outside rin matter may leave the disk and either flow in more radially or be expelled. Particularly for black holes advective flow solutions are discussed where the disk terminates and the flow becomes more spherical at a much larger radius (e.g., Narayan 1997). Whatever the geometry, it is clear that as the characteristic velocities near the compact object are of order (GM/R)1/2 0.5c, the dynamical time scale, the time scale for the motion of matter through∼ the emitting region, is short; τ (r3/GM)1/2 0.1 ms for r=10 km, and 2 ms for r=100km near dyn ≡ ∼ ∼ a 1.4M⊙ neutron star, and 1ms at 100km from a 10M⊙ black hole. So, the significance of millisecond∼ X-ray variability from X-ray binaries is clear: milliseconds is the natural time scale of the accretion process in the X-ray emitting regions, and hence strong X-ray variability on such time scales is nearly certainly caused by the motion of matter in these regions. Orbital motion, neutron-star spin, disk- and neutron-star oscillations are all expected to happen on these time scales. The inner flow is located in regions of spacetime where strong-field general- relativity is required to describe the motion of matter. For that reason one 2 expects to detect strong-field general-relativistic effects in these flows, such as for example the existence of a region where no stable orbits are possible. The precise interactions between the elementary particles in the interior of a neutron star which determine the equation of state (EOS) of supra-nuclear-density matter are not known. Therefore we can not confidently predict the radius of a neutron star of given mass, or the maximum spin rate or mass of neutron stars (e.g., Cook et al. 1994). So, by measuring these macroscopic quantities one constrains the EOS and tests basic ideas about the properties of elementary particles. In summary, the main motivation for studying millisecond variations in X-ray binaries is that their properties depend on untested, or even unknown, properties of spacetime and matter. Three different millisecond phenomena have now been observed in X-ray binaries. Historically, the first to be discovered were the twin kilohertz quasi- periodic oscillations (kHz QPOs), widely interpreted now as due to orbital motion in the inner accretion flow. Then came the burst oscillations, probably due to the spin of a layer in the neutron star’s atmosphere in near-corotation with the neutron star itself. Finally RXTE detected the first true spin frequency of an accreting low-magnetic field neutron star, the long-anticipated accreting millisecond pulsar. In this review, I first examine the millisecond pulsar ( 3), then the burst oscillations ( 4) and finally the kHz QPOs ( 5). We will thus§ be venturing from the (relatively)§ well-understood accreting pulsars§ via the less secure regions of what happens in detail on a neutron star’s surface during the thermonuclear runaway that is an X-ray burst, into the mostly uncharted territory of the innermost accretion flows around neutron stars and black holes, which obvi- ously is “where the monsters are”, but also where the greatest rewards wait. The possibly related phenomena found in black-hole candidates ( 6.1) and at lower frequencies ( 6.3) are discussed next, and in 7 the kHz QPO§ models are summarized. § § 2 Techniques Most of the variability measurements discussed here rely on Fourier analysis of X-ray count-rate time series with sub-millisecond time resolution (van der Klis 1989b). A quasi-periodic oscillation (QPO) in the time series stands out in the power spectrum (the square of the Fourier transform) as a broad, usually Lorentzian peak (in Fig.5 several of such peaks can be seen), characterized by its frequency ν (“centroid frequency”), width λ (inversely proportional to the coherence time of the oscillation) and strength (the peak’s area is proportional to the variance of the QPO signal). The variance is nearly always reported in 3 terms of the root-mean-square of the signal expressed as a fraction of the count rate, the “fractional rms amplitude” r; the coherence often in terms of a quality factor Q = ν/λ. Conventionally, to call a local maximum in a power spectrum a QPO peak one requires Q> 2. Time delays between signals simultaneously detected in different energy bands are usually measured using cross-spectra (the frequency-domain equivalent of the cross-correlation function; van der Klis et al. 1987, Vaughan et al. 1994a, Nowak et al. 1998) and often expressed in terms of a phase lag (time lag multiplied by frequency). The signal-to-noise of a broad power-spectral feature is nσ = 1 2 1/2 2 Ixr (T/λ) (van der Klis 1989b, see van der Klis 1998 for more details), where I is the count rate and T the observing time (assumed 1/λ). Note x ≫ that nσ is proportional to the count rate and to the signal amplitude squared, so that it is sufficient for the amplitude to drop by 50% for the signal-to-noise to go from, e.g., a whopping 6σ to an undetectable 1.5σ – i.e., if a power-spectral feature “suddenly disappears” it may have only decreased in amplitude by a factor of two.

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